/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 49 For exercises \(23-74\), evaluat... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 0: Problem 49

For exercises \(23-74\), evaluate. $$ \frac{11}{12} \div \frac{2}{3} $$

Short Answer

Expert verified
The solution to \(\frac{11}{12} \div \frac{2}{3}\) is \(\frac{11}{8}\).

Step by step solution

01

Understand the division of fractions

In order to divide one fraction by another, you need to multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by swapping the numerator and the denominator.
02

Find the reciprocal

The reciprocal of \(\frac{2}{3}\) is \(\frac{3}{2}\).
03

Multiply the fractions

Now, multiply \(\frac{11}{12}\) by \(\frac{3}{2}\): \[ \frac{11}{12} \times \frac{3}{2} \]
04

Multiply the numerators

Multiply the numerators: \[ 11 \times 3 = 33 \]
05

Multiply the denominators

Multiply the denominators: \[ 12 \times 2 = 24 \]
06

Simplify the resulting fraction

The resulting fraction is \(\frac{33}{24}\). Simplify by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 3: \[ \frac{33 \div 3}{24 \div 3} = \frac{11}{8} \]

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Reciprocal
To understand the reciprocal, remember that it's just flipping a fraction. When you have a fraction like \(\frac{2}{3}\), its reciprocal is \(\frac{3}{2}\). This means the numerator (top number) and the denominator (bottom number) swap places.

Reciprocals are important in division of fractions. Instead of directly dividing fractions, we multiply by the reciprocal of the second fraction.

For example, if you need to evaluate \(\frac{11}{12} \/ \frac{2}{3}\), first find the reciprocal of \(\frac{2}{3}\), which is \(\frac{3}{2}\). Then, instead of division, you move to multiplication. This makes the calculation easier.
Multiplying Fractions
Multiplying fractions is straightforward. You multiply the numerators together and the denominators together.

Let's take the fractions \(\frac{11}{12}\) and \(\frac{3}{2}\). To multiply them, follow these steps:
  • Multiply the numerators: \11 \times 3 = 33\
  • Multiply the denominators: \12 \times 2 = 24\
So, \(\frac{11}{12} \times \frac{3}{2} = \frac{33}{24}\).

This process is much simpler than dividing fractions directly and it works for any two fractions.
Simplifying Fractions
Simplifying fractions means making the fraction as simple as possible. This is done by dividing the numerator and the denominator by their greatest common divisor (GCD).

For our earlier product \(\frac{33}{24}\), we can find the GCD of 33 and 24, which is 3. Now, divide both the numerator and the denominator by 3:
  • Numerator: \(33 \div 3 = 11\)
  • Denominator: \(24 \div 3 = 8\)
Thus, \(\frac{33}{24}\) simplifies to \(\frac{11}{8}\), which is the simplest form of the fraction.

Simplification makes it easier to understand and use fractions in further calculations.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

For exercises \(47-58\), rewrite the percent as a decimal number. $$ 9.6 \% $$

For exercises \(47-58\), rewrite the percent as a decimal number. $$ 2 \% $$

If 8 out of 200 bills are overdue, find the percent of the bills that are overdue.

$$ -12-5 $$

$$ \text { Round } 0.0053 \text { to the nearest thousandth. } $$
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.